Abstract : This report verifies that conventional control limits for the Shewhart control chart for range (R chart) provide an unreliable basis for indicating when the process has gone out of statistical control unless these limits are based on a fairly large number of subgroups. A new method then is developed for using a small number of subgroups to set reliable control limits for the R chart. These limits have the property that they yield the desired probability of a Type I on each subsequent subgroup. Tables for calculating such limits are presented. The author previously has proposed an analogous method for setting control limits for an average chart. Since the R chart usually is used in conjunction with an average chart, these results enable one to set statistically sound control limits for both charts as soon as desired. This permits the valid use of both charts during the crucial initiation of a new process, during the start-up of a process just brought into statistical control again, or for a process whose total output is small. (Author)